Mathematics: If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) g(1) = 4 h(1) = 7 g (1) = 5 h (1) = −3 fx(4, 7) = 4 fy(4, 7) = 7 find dz/dt when t = 1.

If z = f(x, y), where f is differentiable, and

Ответ:

xojade

13.03.2022

By the chain rule,

$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}$

but since

is essentially a function of

alone, we can the derivative more succinctly as

z'(t)=f_x(g(t),h(t))g'(t)+f_y(g(t),h(t))h'(t)

z'(1)=f_x(g(1),h(1))g'(1)+f_y(g(1),h(1))h'(1)

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Ответ:

janiyahmcgolley

23.06.2020

Mathematics

Estimates: $65

Actually: $73

65 / 73

= 0.9 (round to nearest tenth)

I hope this helps, I may be wrong. Somebody can correct me if I am wrong. :)

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If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) g(1) = 4 h(1) = 7 g' (1) = 5 h' (1) = −3 fx(4, 7) = 4 fy(4, 7) = 7 find dz/dt when t = 1.

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